Problem: A group of adults and kids went to see a movie. Tickets cost $$5.50$ each for adults and $$4.00$ each for kids, and the group paid $$62.00$ in total. There were $6$ fewer adults than kids in the group. Find the number of adults and kids in the group.
Solution: Let $x$ equal the number of adults and $y$ equal the number of kids. The system of equations is then: ${5.5x+4y = 62}$ ${x = y-6}$ Solve for $x$ and $y$ using substitution. Since $x$ has already been solved for, substitute ${y-6}$ for $x$ in the first equation. ${5.5}{(y-6)}{+ 4y = 62}$ Simplify and solve for $y$ $ 5.5y-33 + 4y = 62 $ $ 9.5y-33 = 62 $ $ 9.5y = 95 $ $ y = \dfrac{95}{9.5} $ ${y = 10}$ Now that you know ${y = 10}$ , plug it back into ${x = y-6}$ to find $x$ ${x = }{(10)}{ - 6}$ ${x = 4}$ You can also plug ${y = 10}$ into ${5.5x+4y = 62}$ and get the same answer for $x$ ${5.5x + 4}{(10)}{= 62}$ ${x = 4}$ There were $4$ adults and $10$ kids.